CN109508444B - Quick tracking method for interactive multimode generalized label multi-Bernoulli under interval measurement - Google Patents

Quick tracking method for interactive multimode generalized label multi-Bernoulli under interval measurement Download PDF

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CN109508444B
CN109508444B CN201811549885.5A CN201811549885A CN109508444B CN 109508444 B CN109508444 B CN 109508444B CN 201811549885 A CN201811549885 A CN 201811549885A CN 109508444 B CN109508444 B CN 109508444B
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吴孙勇
董续东
赵君
蔡如华
孙希延
纪元法
严素清
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Guilin University of Electronic Technology
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Abstract

The invention discloses a quick tracking method of interactive multimode generalized label multi-Bernoulli under interval measurement, which combines the interactive multimode method with a quick algorithm idea, firstly realizes the transfer prediction of all particles to different models by combining an interval measurement generalized likelihood function aiming at a target sampling particle prediction stage under the framework of generalized label multi-Bernoulli filtering, then carries out model interaction on the particles by calculating model weight probability, and then updates the particles after the model interaction by a GLMB filtering updating equation. On the basis, a quick implementation method is combined, prediction and updating are combined, only one truncation process is needed for each iteration, the calculation amount of the algorithm is reduced, and the problem of detection and tracking of multiple maneuvering targets is finally solved.

Description

Quick tracking method for interactive multimode generalized label multi-Bernoulli under interval measurement
Technical Field
The invention relates to the technical field of target tracking, in particular to a quick tracking method of an interactive multimode generalized label multi-Bernoulli under interval measurement.
Background
The movement of a non-maneuvering object can be described by a fixed model, but to describe the movement of a maneuvering object, it may be necessary to combine moving models with different maneuvering characteristics. As the mobile target tracking technology receives more and more extensive attention, the requirements on the mobile target tracking technology are higher and higher. Multi-motorized object tracking has become an extremely difficult problem in the field of object tracking.
The paper "box particle generalized label multi-bernoulli filtering target tracking algorithm" (journal of the university of transport, west ann, 2017,51 (10): 107-112.) published by the scarp proposes a box particle generalized label multi-bernoulli tracking algorithm. The algorithm approximates the probability density of a single target state by using a box particle filter algorithm, namely, the probability density of the single target state is fitted by using a group of uniform distributions with weights; and finally, predicting and updating the probability density of the multiple target states through generalized label multi-Bernoulli filtering, estimating the position and the speed of the single target from the updated probability density of the multiple target states, and realizing track tracking due to the fact that the labels of the single target are different. The algorithm has the disadvantage that the strong maneuvering target cannot be effectively tracked.
Vo et al, in the published paper "A Generalized labelled Multi-Bernoulli Filter f or Maneuvering Targets" (19 th International Conference on Information function on), proposed a motorized target tracking algorithm for Generalized label-PolyBernoulli particle Filtering (GLMB) by combining the interactive multimodal concept with the Label-PolyBernoulli Random Finite Set (RFS) theory, and given the implementation of Gaussian Mixture (GM). The algorithm can track the tracks of different targets while estimating the state of multiple maneuvering targets. The disadvantage of the algorithm is that due to the combination explosion problem in the strong clutter and multi-target environment, the implementation of the GLMB filter faces huge computational complexity.
Vo et al, in a published paper "An efficiency evaluation of the Generalized sampled Multi-Bernoulli Filter" (IEEE Transactions on Signal Processing,2017,65 (8): 1975-1987), proposes a GLMB filtering density truncation algorithm based on Gibbs sampling, integrates prediction and update into one step, and realizes Efficient Implementation of GLMB filtering. The disadvantage of this algorithm is that in many practical applications, the standard metrology model is not sufficient. Although the sensor detection report is a point measurement, the actual measurement is affected by the unknown boundary error distribution, so that the non-standard measurement needs to be performed in the form of interval measurement.
Disclosure of Invention
The invention aims to solve the problem of target tracking loss when a target is greatly maneuvered under interval measurement by the conventional multi-maneuvering target tracking method, and provides a quick tracking method of interactive multimode generalized label multi-Bernoulli under interval measurement.
The basic idea of the invention is as follows: the method is characterized in that an interactive multimode method is combined with a fast algorithm idea, firstly, under the framework of generalized label multi-Bernoulli filtering, a generalized likelihood function is measured in combination with an interval aiming at a target sampling particle prediction stage, the transfer prediction of all particles to different models is realized, then model interaction is carried out on the particles by calculating model weight probability, and then the particles after model interaction are updated through a GLMB filtering updating equation. On the basis, a quick implementation method is combined, prediction and updating are combined, only one truncation process is needed for each iteration, the calculation amount of the algorithm is reduced, and the problem of detection and tracking of multiple maneuvering targets is finally solved.
In order to solve the problems, the invention is realized by the following technical scheme:
the quick tracking method of the interactive multimode generalized label multi-Bernoulli under interval measurement comprises the following steps:
step 1, setting state parameters of target particles at an initial moment according to a target motion scene, taking the set state parameters as initial distribution of the target particles, sampling a fixed number of initially distributed target particles, and representing the initially distributed target particles in a parameter set form of a label Bernoulli random set to obtain posterior distribution of the label Bernoulli random set of the initially sampled particles at the initial moment;
step 2, predicting the target sampling particles by using the posterior distribution of the target sampling particle label multi-Bernoulli random set at the previous moment and the interval measurement data at the previous moment by using an interactive multimode method to obtain the posterior distribution of the target sampling particle label multi-Bernoulli random set predicted at the current moment;
step 3, calculating a generalized likelihood function of each target sampling particle by using interval measurement data at the current moment, and updating posterior distribution of the target sampling particle label Bernoulli random set predicted at the current moment by using a generalized label Bernoulli filter according to the generalized likelihood function to obtain the posterior distribution of the updated target sampling particle label Bernoulli random set at the current moment;
step 4, selecting posterior distribution of the target sampling particle label multi-Bernoulli random set updated at the current moment, of which the label weight is larger than a given threshold value, from the posterior distribution of the target sampling particle label multi-Bernoulli random set updated at the current moment obtained in the step 4, and taking the posterior distribution as the posterior distribution of the target sampling particle label multi-Bernoulli random set truncated at the current moment;
step 5, respectively calculating the posterior distribution potentials of the truncated target sampling particle label multi-Bernoulli random set at the current moment obtained in the step 5, and finding out an index N corresponding to the maximum potential; selecting the posterior distribution of N-1 current-moment truncated target sampling particle label Bernoulli random sets with larger label weight from the posterior distribution of the current-moment truncated target sampling particle label Bernoulli random sets obtained in the step 5, and taking the posterior distribution as the posterior distribution of the final current-moment target sampling particle label Bernoulli random set;
step 6, calculating the weighted sum of the posterior distribution of the final target sampling particle label multi-Bernoulli random set at the current moment, and taking the weighted sum result as the estimated target state at the current moment;
and 7, judging whether all the moments are processed or not: if yes, outputting the estimated target state at the current moment; otherwise, step 2 is executed to process the next moment.
Compared with the prior art, the invention has the following characteristics:
1. the multi-model concept and the fast algorithm idea are embedded into the generalized label multi-Bernoulli algorithm, the particle filtering method is adopted, the track of the target can be accurately tracked, the number of the targets can be accurately estimated, the calculation amount of the algorithm is far smaller than that of the interactive multimode generalized label multi-Bernoulli algorithm, and the operation performance is improved.
2. The method combines interactive multimode, realizes the transfer prediction of all particles to different models aiming at the target sampling particle prediction stage, and then performs model interaction on the particles by calculating the model weight probability, thereby realizing the detection and tracking of the maneuvering target and overcoming the tracking loss problem existing in the prior art for tracking the maneuvering target.
3. The fast algorithm idea is combined, the traditional sensor measuring model is not adopted in the target measuring model, the sensor outputs interval measurement, the interval measurement is used for making up any point measuring defect, factors such as unstable maneuverability of a maneuvering target and the like are comprehensively considered, the fast algorithm integrates prediction and updating to one step, only one truncation process is needed for each iteration, the calculated amount of the algorithm is greatly reduced, and the detection and tracking of the maneuvering target under the interval measurement are effectively realized.
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FIG. 1 is a flow chart of a fast tracking method of an interactive multimode generalized label multi-Bernoulli under interval measurement.
Fig. 2 is a simulation diagram of the present embodiment, wherein (a) is a target motion trajectory diagram, (b) is a target track tracking result diagram, (c) is a target number tracking effect diagram, (d) is a target number tracking error diagram, (e) is a target OSPA distance tracking error diagram, (f) is a target OSPA position tracking error diagram, and (g) is a target OSPA potential tracking error diagram.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings in conjunction with specific examples.
Aiming at the problems of uncertainty of interval measurement and uncertainty of target mobility, the method predicts the sampling particles of each target state in the filter by using an interactive multi-model method on the basis of a generalized label multi-Bernoulli filter, and updates the prediction particles by introducing a generalized likelihood function and combining a GLMB filter updating strategy. On the basis, a quick implementation method is combined, prediction and updating are combined, only one truncation process is needed for each iteration, the calculation amount of the algorithm is reduced, the method can effectively detect and track the maneuvering multiple targets under the interval measurement environment, and the target state and the number are more accurately estimated.
A quick tracking method of interactive multimode generalized label multi-Bernoulli under interval measurement comprises the following specific steps:
step 1, initializing a target state.
According to the target motion scene, an initial moment GLMB track table is set, and the initial moment GLMB track table comprises target particles (including continuous survival particles and new particles) and state parameters, namely target positions, speeds, weights, model probabilities, track labels and track association history. Initializing GLMB component hypothesis weights, hypothesis labels, hypothesis potentials, and potential distributions. A fixed number of initial viable and nascent particles are sampled with a gaussian distribution using the above-set parameters as the initial distribution of the target and represented in the form of a parameter set labeled as a multi-bernoulli random set.
The initial particle sampling procedure was as follows:
Figure BDA0001910372630000041
wherein, P 0 Is the covariance of the target state at the initial time,
Figure BDA0001910372630000042
is a state x 0 The corresponding label is marked with a corresponding label,
Figure BDA0001910372630000043
is the set of tags at the initial time.
Let initial time k =0, the initial distribution of the target is represented by the parameter set of the gaussian particle label-multiple-bernoulli-random set as follows:
Figure BDA0001910372630000044
wherein H is a target space, H is a target,
Figure BDA0001910372630000045
the hypothesis weight of the initial moment GLMB track table hypothesis label is represented;
Figure BDA0001910372630000046
representing the model weight probability of the jth target sample particle (labeled l) at the initial time,
Figure BDA0001910372630000047
p is the number of models;
Figure BDA0001910372630000048
indicating the state of the jth target sample particle at the initial time,
Figure BDA0001910372630000049
x 0 the abscissa representing the target at the initial moment,
Figure BDA00019103726300000410
indicating the horizontal velocity, y, of the target at the initial moment 0 The ordinate of the object at the initial moment is shown,
Figure BDA00019103726300000411
the vertical speed of the target at the initial moment is shown, and T shows transposition operation;
Figure BDA00019103726300000412
representing the state weight corresponding to the jth target sampling particle state at the initial moment;
Figure BDA00019103726300000413
representing the target number of sample particles at the initial time.
And 2, predicting and updating the target state.
The state of the target at the time k can be represented by a 4-dimensional vector
Figure BDA00019103726300000414
Is represented by (x) k ,y k )、
Figure BDA00019103726300000415
Respectively, the position and the velocity of the target at the time k.When the target is a maneuvering target, the motion model changes along with time, and the motion equation is as follows:
x k ＝f k-1 (x k-1 ,s k )+v k-1 (s k )
wherein f is k-1 Equation of state transition, s, representing the target at time k k Model variable representing time k, v k-1 Representing state noise.
The posterior distribution of the target sampling particle label multi-Bernoulli random set at the k-1 moment is assumed as follows:
Figure BDA00019103726300000416
the persistent survival particle signature-the multi-bernoulli random set-is expressed as:
Figure BDA00019103726300000417
the k moment new particle label is a multi-Bernoulli random set
Figure BDA00019103726300000418
Then the target sampling particle label multi-bernoulli random set predicted at the moment k is:
Figure BDA00019103726300000419
Figure BDA00019103726300000420
representing the state prediction of the persistent survival particles under the model s from the moment k-1 to the moment k,
Figure BDA00019103726300000421
the state of the sampled particle representing the new target at time k is predicted under model s,
Figure BDA00019103726300000422
representing the model weight probability of the sustained-survival particles at time k under the model s,
Figure BDA0001910372630000051
representing the model weight probability under the model s at the moment of the sampled particle k of the new object,
Figure BDA0001910372630000052
representing the weighted prediction of the surviving particles under the model s from time k-1 to time k,
Figure BDA0001910372630000053
and predicting the weight of the sampled particles representing the new target at the k moment under the model s.
The specific prediction method can be accomplished by the following steps.
And 2.1, carrying out posterior distribution on the target sampling particle labels updated at the k-1 moment in a multi-Bernoulli random set, and resampling to obtain sampling samples of the survival particles at the k-1 moment, wherein the sampling samples comprise:
Figure BDA0001910372630000054
2.2, setting 4 kinds of birth particle components according to Gaussian distribution, and sampling together
Figure BDA0001910372630000055
And (4) generating new particles.
Figure BDA0001910372630000056
Wherein N (m) i P), i =1,2,3,4 is the new density at the target k instant, and the specific process is expressed as follows:
particles are uniformly generated around the particles according to the mean value and variance of each birth particle component, and 4 birth particle components are co-generated
Figure BDA0001910372630000057
And (4) generating new particles.
Step 2.3, resampling the survival particle sample obtained at the time k-1, namely
Figure BDA0001910372630000058
Survival particles are predicted by combining an interactive multimode method, and the specific mode is expressed as follows:
Figure BDA0001910372630000059
wherein, F s,k The state transfer equation corresponding to the model s is that s =1, \8230, p and p are the total number of the models, v k Is state noise.
Calculating the probability of the model weight:
Figure BDA00019103726300000510
wherein,
Figure BDA00019103726300000511
is the probability of the prediction model that the model,
Figure BDA00019103726300000512
T r:,s for the h-th column of the model transition probability matrix,
Figure BDA00019103726300000513
is the predicted particle interval measurement generalized likelihood function corresponding to the model s.
Particles predicted from each model
Figure BDA00019103726300000514
And model weight probability
Figure BDA00019103726300000515
Interactive multi-model hybrid particles can be obtained, wherein
Figure BDA00019103726300000516
The specific calculation is as follows:
Figure BDA00019103726300000517
and 2.4, calculating the predicted states and weights of the survival targets and the birth targets:
Figure BDA00019103726300000518
Figure BDA00019103726300000519
Figure BDA00019103726300000520
Figure BDA0001910372630000061
wherein
Figure BDA0001910372630000062
And 2.5, combining the labeled weight particles:
Figure BDA0001910372630000063
and 2.6, updating the target state.
Assume that the predicted target sample particle at time k is represented as:
Figure BDA0001910372630000064
the updated posterior distribution of the target sampling particles is:
Figure BDA0001910372630000065
wherein,
Figure BDA0001910372630000066
representing the jth target sample particle state prediction from time k-1 to time k,
Figure BDA0001910372630000067
representing the update of the jth target sampling particle state at the k moment;
Figure BDA0001910372630000068
representing a prediction of the weight of the jth target sample particle from time k-1 to time k,
Figure BDA0001910372630000069
updating the weight of the jth target sampling particle at the k moment;
Figure BDA00019103726300000610
representing the predicted target number of sample particles at time k,
Figure BDA00019103726300000611
target sample particle number at time k.
And updating the target sampling particle label multi-Bernoulli random set predicted at the k moment by using the generalized likelihood function of the target random set at the k moment to obtain the posterior distribution of the target sampling particle label multi-Bernoulli random set at the k moment.
The specific updating method can be accomplished by the following steps.
Step 2.6.1, calculating the generalized likelihood function corresponding to each predicted target sampling particle by using the interval measurement data of the current time, supposing that the generalized likelihood function corresponding to each predicted target sampling particle is considered at X k The detection is independent, the clutter is irrelevant to the detection, and the multi-target likelihood is specifically calculated as follows:
Figure BDA00019103726300000612
wherein
Figure BDA00019103726300000613
Is a function such that θ is satisfied when i = j k (i)＝θ k (j) And if the average value of the clutter is more than 0, and the method takes the value of lambda =10. Wherein
Figure BDA00019103726300000614
The generalized likelihood function of a single target is
Figure BDA00019103726300000615
Where N (y; μ, P) represents a Gaussian probability density function with a mean of μ and a covariance of P. Sigma-delta measurement noise v k Of (a) covariance, i.e. p v (v) N (v; 0, Σ). In addition, the method can be used for producing a composite material
Figure BDA00019103726300000616
z＝[z l ,z r ]。
And 2.6.2, updating and calculating the weight of each predicted target particle at the k moment according to the interval measurement likelihood function:
Figure BDA0001910372630000071
wherein,
Figure BDA0001910372630000072
prediction weight for each predicted target particle, where M s,k Representing a set of model variables at time k, M s,k ＝{s 1 ,…,s k }。
And 3, component truncation.
And selecting the posterior distribution of the target sampling particle label multi-Bernoulli random set updated at the current moment, of which the label weight is greater than a given threshold value, from the posterior distribution of the target sampling particle label multi-Bernoulli random set updated at the current moment as the posterior distribution of the target sampling particle label multi-Bernoulli random set truncated at the current moment.
In general, in the GLMB algorithm, the number of assumed trajectories at the previous time is truncated twice to the next time, and the truncation operation is required for the prediction and update of the assumed trajectories. In order to improve the algorithm operation efficiency, the algorithm integrates the steps of prediction and updating, only once truncation is needed, and the operation speed of the algorithm is greatly improved.
The posterior distribution of the target sampling particle label multi-Bernoulli random set at the k-1 moment is assumed as follows:
Figure BDA0001910372630000073
the posterior distribution of the target sampling particle label multi-Bernoulli random set at the time k is as follows:
Figure BDA0001910372630000074
wherein H is the index space, H is the index, and the total number of components from the k-1 moment is H k-1 The total number of components up to k is H k Only one truncation operation is needed, and the computational complexity of the algorithm is greatly reduced.
And 4, estimating the state.
We use a suboptimal version of the edge multi-target estimation, a posteriori estimation of the maximum potential. The average estimate of the multi-target state depends on the estimated potential, and a potential distribution is calculated for the updated target particles.
Respectively calculating posterior distribution potentials of the truncated target sampling particle label multi-Bernoulli random set at the current moment, and finding out an index N corresponding to the maximum potential k +1; selecting N with larger label weight from posterior distribution of target sampling particle label multi-Bernoulli random set truncated at current moment k The posterior distribution of the truncated target sampling particle label multi-Bernoulli random set at the current moment,and the posterior distribution of the particle label multi-Bernoulli random set is taken as the final target sampling at the current moment.
And calculating the weighted sum of the states of the target sampling particles by adopting a weighting method according to the posterior distribution of the target sampling particle label multi-Bernoulli random set at the current moment, wherein the weighted sum is used as the real target state at the current moment. If the number of the targets corresponding to the maximum posterior potential of the target is estimated to be N k . The state estimate is specifically calculated as follows:
Figure BDA0001910372630000081
wherein,
Figure BDA0001910372630000082
for updated particles for which the posterior maximum potential corresponds to the target sample particle of the hypothetical trajectory,
Figure BDA0001910372630000083
indicating the update weight of the corresponding update particle. x is the number of k,i And estimating the state of the ith target at the current moment.
And 5, judging whether all the moments are processed or not, if so, executing the step 6, otherwise, executing the step 2 and processing the next moment.
And 6, ending.
On the basis of generalized label multi-Bernoulli filtering, the method uses an interactive multi-model method to predict the sampling particles of each target state in the filter, and then substitutes the predicted particles into the GLMB algorithm to update and estimate the target existence probability and distribution density. The invention can effectively detect and track multiple maneuvering targets under the condition of interval measurement environment, and realizes the estimation of the target state and the number.
The effect of the present invention will be further explained with reference to the simulation diagram of fig. 2.
Simulation conditions are as follows: the invention adopts MATLAB R2014a software to complete simulation on a computer with an Intel (R) Core (TM) i3-2370M CPU @2.40GHz processor.
Simulation fieldSetting a scene: in order to verify that the rapid implementation algorithm of the interactive multimode generalized mark Bernoulli filter under interval measurement can accurately detect and track the weak and small maneuvering targets, the simulation experiment scene of the invention is [ -2000,2000 [ -2000]×[0,2000]m 2 In two-dimensional space, the whole simulation process lasts for 100 seconds, and the birth death time and the motion state of each target are shown in table 1.
TABLE 1
Target Linear motion at uniform speed Left turn motion Right hand turning motion
1 1～20s 21～65s 66～100s
2 10～25s 26～70s 71～100s
3 15～35s 36～65s 66～100s
4 20～35s 36～57s 58～80s
5 60～70s 71～95s 96～100s
The target state equation is:
Figure BDA0001910372630000084
wherein
Figure BDA0001910372630000088
Representing the state transition matrix for the motion model s, s =1,2,3.
Figure BDA0001910372630000085
Are all zero mean white gaussian noise. Definition of
Figure BDA0001910372630000089
Is a model of uniform linear motion,
Figure BDA00019103726300000810
in order to move in a left-hand turn,
Figure BDA00019103726300000811
a right turn motion.
Figure BDA0001910372630000086
ω (2) ＝-0.04rad/s，ω (3) ＝0.1rad/s。
Figure BDA0001910372630000087
To represent the covariance matrix as Q j Is a zero-mean white gaussian noise of (1),
Figure BDA0001910372630000091
t denotes a sampling period. Wherein σ v ＝4m/s 2 ，
Figure BDA0001910372630000092
The measurement equation is:
Figure BDA0001910372630000093
wherein,
Figure BDA0001910372630000094
represents the measurement likelihood function (x) k ,y k ) Indicating the location of the target. Wherein omega k Is zero mean and covariance matrix of
Figure BDA0001910372630000095
White Gaussian noise of (1), where σ r =2.5m and σ θ =0.25 °. The sensor provides interval measurements having an interval length of Δ = [ ] r ,Δ θ ] T In which Δ r =50m and Δ θ =4 ° is the interval length of the range and azimuth angle, respectively.
Giving the accurate positions of five targets when the generalized label multi-Bernoulli filter is initialized, wherein the initial state of the targets is x 1 ＝[1000,-10,1500,-10]，x 2 ＝[-250,20,1000,3]，x 3 ＝[-1500,11,250,10]，x 4 ＝[250,11,750,5]，x 5 ＝[1000,-50,1500,0]. The relevant simulation parameters are set as follows: p is a radical of formula D,k =0.98 and p S,k =0.99, clutter mean λ =10. Target initial model weight probability
Figure BDA0001910372630000096
To be made intoProving the simulation effect, truncating the threshold value H th ＝1×10 -15 In the case of a clutter rate of λ =10, the number of surviving and newly born particles was subjected to 100 monte carlo experiments per 100 particles. An OSPA (Optimal Sub-Pattern Assignment) distance of the target is calculated, and the OSPA parameter is set to c =100m, p =2. Fig. 2 (a) and 2 (b) show a motion state of a target and a track tracking result when the clutter ratio is λ =10, respectively. The circles in the trace of fig. 2 (a) represent the target initial positions and the triangles represent the target final positions. FIG. 2 (b) is the result of track following of a target; as can be seen from fig. 2 (b), the method of the present invention can deal with the maneuvering problem of the target, and can track the accurate position of the target at the moment when the target turns. FIGS. 2 (c) and 2 (d) are a tracking effect map and a potential error map of a target potential, respectively; as can be seen from fig. 2 (c) and 2 (d), the method of the present invention has the advantages of relatively accurate estimation of the target potential, relatively stable estimation error and smaller than the IMM-GLMB algorithm (interactive multimode generalized label-based multi-bernoulli filter under interval measurement) and the IMM-LMB algorithm (interactive multimode label-based multi-bernoulli filter under interval measurement) without considering individual time instants. FIG. 2 (e), FIG. 2 (f) and FIG. 2 (g) show the OSPA range tracking error plot, the OSPA location tracking error plot and the OSPA potential tracking error plot, respectively, for a target with 100 surviving and newly born particles; as can be seen from FIG. 2 (e), when the number of targets is increased, the target distance tracking error of the method of the present invention is relatively stable and smaller than the IMM-GLMB algorithm and the IMM-LMB algorithm; as can be seen from FIG. 2 (f), when the target position is estimated, the tracking performance is further improved, the estimation deviation of the target at the maneuvering moment is reduced, and the filtering performance is more stable than that of the IMM-GLMB algorithm and the IMM-LMB algorithm; as can be seen from FIG. 2 (g), when the number of targets is estimated, the tracking performance of the method is obviously better than that of the IMM-GLMB algorithm and the IMM-LMB algorithm, and when the number of the targets is increased, the number of the targets can be well tracked.
In conclusion, from the analysis of the simulation effect diagram, the method for rapidly realizing the tracking of the interactive multimode generalized label multi-bernoulli filter under the interval measurement provided by the invention realizes the detection and tracking of maneuvering multiple targets under the interval measurement. The method has the advantages of high target tracking precision, good tracking performance and relatively superior performance to an interactive multimode generalized label multi-Bernoulli filter, an interactive multimode probability hypothesis density filter and an interactive multimode probability hypothesis density filter.
It should be noted that, although the above-mentioned embodiments of the present invention are illustrative, the present invention is not limited thereto, and thus the present invention is not limited to the above-mentioned embodiments. Other embodiments, which can be devised by those skilled in the art in light of the teachings of the present invention, are considered to be within the scope of the present invention without departing from its principles.

Claims (1)

1. The quick tracking method of the interactive multimode generalized label multi-Bernoulli under interval measurement is characterized by comprising the following steps:
step 1, setting state parameters of target particles at an initial moment according to a target motion scene, taking the set state parameters as initial distribution of the target particles, sampling a fixed number of initially distributed target particles, and expressing the initially distributed target particles in a parameter set form of a label Bernoulli random set to obtain the posterior distribution of the label Bernoulli random set of the initially sampled particles, wherein the posterior distribution of the label Bernoulli random set of the initially sampled particles is as follows:
Figure FDA0003863532630000011
in the formula, H is a target space, H is a target,
Figure FDA0003863532630000012
the method comprises the steps of representing the hypothetical weight of a generalized label multi-Bernoulli particle filter track table hypothetical label at an initial moment;
Figure FDA0003863532630000013
indicating the state of the jth target sample particle at the initial time,
Figure FDA0003863532630000014
x 0 the abscissa representing the target at the initial moment,
Figure FDA0003863532630000015
indicating the horizontal velocity, y, of the target at the initial moment 0 The ordinate of the object at the initial moment is shown,
Figure FDA0003863532630000016
the vertical speed of the target at the initial moment is shown, and T shows transposition operation;
Figure FDA0003863532630000017
representing the model weight probability of the jth target sample particle at the initial time,
Figure FDA0003863532630000018
p is the number of models;
Figure FDA0003863532630000019
representing the state weight corresponding to the jth target sampling particle state at the initial moment;
Figure FDA00038635326300000110
representing a target number of sample particles at an initial time; l is a label;
step 2, predicting the target sampling particles by using the posterior distribution of the target sampling particle label multi-Bernoulli random set at the previous moment and the interval measurement data at the previous moment by using an interactive multimode method, and obtaining the posterior distribution of the target sampling particle label multi-Bernoulli random set predicted at the current moment as follows:
Figure FDA00038635326300000111
in the formula,
Figure FDA00038635326300000112
representing the state prediction of the persistent survival particles under the model s from the moment k-1 to the moment k,
Figure FDA00038635326300000113
representing the model weight probability of the sustained-survival particles at time k under the model s,
Figure FDA00038635326300000114
representing the weighted prediction of the surviving particles under the model s from time k-1 to time k,
Figure FDA00038635326300000115
indicates the number of persistent particles;
Figure FDA00038635326300000116
the state of the sampled particle representing the new target at time k is predicted under model s,
Figure FDA00038635326300000117
representing the model weight probability under the model s at the moment of the new object's sampled particle k,
Figure FDA00038635326300000118
predicting the weight of the sampled particles representing the new target at the moment k under a model s;
Figure FDA00038635326300000119
represents the number of new particles; l is a label;
the specific prediction method can be completed by the following steps:
step 2.1, carrying out posterior distribution on the target sampling particle label after updating at the time k-1, and resampling to obtain a sampling sample of the survival particles at the time k-1;
step 2.2, according to the Gaussian distribution,setting 4 kinds of birth particle components, and co-sampling
Figure FDA00038635326300000120
A new particle;
step 2.3, live particles are predicted by combining a live particle sampling sample obtained by resampling at the k-1 moment with an interactive multimode method, and particles predicted by each model
Figure FDA00038635326300000121
And model weight probability
Figure FDA00038635326300000122
Obtaining interactive multi-model mixed particles, and specifically calculating as follows:
Figure FDA0003863532630000021
wherein,
Figure FDA0003863532630000022
Figure FDA0003863532630000023
is the probability of the prediction model that the model,
Figure FDA0003863532630000024
T r:,h for the h-th column of the model transition probability matrix,
Figure FDA0003863532630000025
is a predicted particle interval measurement generalized likelihood function corresponding to the model s,
Figure FDA0003863532630000026
F s,k the state transfer equation corresponding to the model s is that s =1, \8230, p and p are the total number of the models, v k Is state noise;
Figure FDA0003863532630000027
step 2.4, calculating the prediction states and weights of the survival targets and the birth targets:
Figure FDA0003863532630000028
Figure FDA0003863532630000029
Figure FDA00038635326300000210
Figure FDA00038635326300000211
wherein
Figure FDA00038635326300000212
Step 2.5, combining the labeled weight particles:
Figure FDA00038635326300000213
step 3, calculating a generalized likelihood function of each target sampling particle by using the interval measurement data at the current moment, updating the posterior distribution of the target sampling particle label Bernoulli random set predicted at the current moment by using a generalized label Bernoulli filter according to the generalized likelihood function, and obtaining the posterior distribution of the target sampling particle label Bernoulli random set updated at the current moment as follows:
Figure FDA00038635326300000214
in the formula,
Figure FDA00038635326300000215
representing the update of the jth target sample particle state at time k,
Figure FDA00038635326300000216
representing the update of the weight of the jth target sampling particle at the k moment;
Figure FDA00038635326300000217
representing the predicted target number of sample particles at time k,
Figure FDA00038635326300000218
representing the target number of sample particles at time k;
the specific updating method can be completed by the following steps:
step 3.1, calculating a generalized likelihood function corresponding to each predicted target sampling particle by using the interval measurement data at the current moment, wherein the multi-target likelihood is specifically calculated as follows:
Figure FDA00038635326300000219
step 3.2, updating and calculating the weight of each predicted target particle at the k moment according to the interval measurement likelihood function:
Figure FDA0003863532630000031
in the formula,
Figure FDA0003863532630000032
is a function such that θ is satisfied when i = j k (i)＝θ k (j) Is more than 0, lambda is the clutter mean value,
Figure FDA0003863532630000033
M s,k representing a set of model variables at time k, M s,k ＝{s 1 ,…,s k }；
And 4, selecting posterior distribution of the target sampling particle label multi-Bernoulli random set updated at the current moment with the label weight larger than a given threshold value from the posterior distribution of the target sampling particle label multi-Bernoulli random set updated at the current moment obtained in the step 4, wherein the posterior distribution of the target sampling particle label multi-Bernoulli random set truncated at the current moment is as follows:
Figure FDA0003863532630000034
in the formula, hk is the total number of components of the index space H at the moment k, and H is an index;
Figure FDA0003863532630000035
the generalized label multi-bernoulli particle filter trajectory table representing the k time instant assumes the assumed weights of the labels,
Figure FDA0003863532630000036
representing the state of the jth target sample particle at time k,
Figure FDA0003863532630000037
representing the model weight probability of the jth target sample particle at time k,
Figure FDA0003863532630000038
representing the state weight corresponding to the jth target sampling particle state at the moment k;
Figure FDA0003863532630000039
representing a target sampling particle number at time k; l is a label;
step 5, respectively calculating the posterior distribution potentials of the truncated target sampling particle label multi-Bernoulli random set at the current moment obtained in the step 5, and finding out an index N corresponding to the maximum potential; selecting the posterior distribution of N-1 current-moment truncated target sampling particle label Bernoulli random sets with larger label weight from the posterior distribution of the current-moment truncated target sampling particle label Bernoulli random sets obtained in the step 5, and taking the posterior distribution as the posterior distribution of the final current-moment target sampling particle label Bernoulli random set;
step 6, calculating the weighted sum of the posterior distribution of the final target sampling particle label multi-Bernoulli random set at the current moment, and taking the weighted sum result as the estimated target state at the current moment; the state estimation is specifically calculated as follows:
Figure FDA00038635326300000310
wherein x is k,i For the state estimate of the ith target at the current time,
Figure FDA00038635326300000311
for the updated particle of the target sample particle for which the posterior maximum potential corresponds to the hypothetical trajectory,
Figure FDA00038635326300000312
representing an update weight of a corresponding update particle;
Figure FDA00038635326300000313
representing the target number of sample particles at time k; l is a label; n is a radical of k The number of targets corresponding to the maximum posterior potential;
and 7, judging whether all the moments are processed or not: if yes, outputting the estimated target state at the current moment; otherwise, step 2 is executed to process the next moment.
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